Re: the ellipse and the circle

*To*: mathgroup at smc.vnet.net*Subject*: [mg69219] Re: the ellipse and the circle*From*: Urijah Kaplan <uak at sas.upenn.edu>*Date*: Sun, 3 Sep 2006 01:39:02 -0400 (EDT)*Organization*: University of Pennsylvania*References*: <200609011041.GAA25668@smc.vnet.net> <edadmf$pef$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

After using those options, try using FullSimplify[Reduce[]] instead of Solve[] on your equations, and see if you like the form of those answers. --Urijah > > Your equations are equivalent to finding the roots of a 4th order > polynomial. By default, Solve will use radicals to express the root of a > quartic polynomial, and hence yields an enormous and useless result in > this case. We can control this behavior by changing the options of Roots: > > SetOptions[Roots, Cubics -> False, Quartics -> False] > > Now using Solve will produce much smaller results at the cost of > containing explicit Root objects. > > Carl Woll > Wolfram Research > >> In[1]:= >> $Version >> Out[1]= >> "5.1 for Microsoft Windows (October 25, 2004)" >> In[3]:= >> e = x^2/a^2 + y^2/b^2 == 1 >> Out[3]= >> x^2/a^2 + y^2/b^2 == 1 >> In[4]:= >> x0 = a*Cos[\[Theta]] >> Out[4]= >> a*Cos[\[Theta]] >> In[5]:= >> y0 = b*Sin[\[Theta]] >> Out[5]= >> b*Sin[\[Theta]] >> In[6]:= >> c = (x - x0)^2 + (y - y0)^2 == r^2 >> Out[6]= >> (x - a*Cos[\[Theta]])^2 + (y - b*Sin[\[Theta]])^2 == r^2 >> In[7]:= >> Solve[{e, c}, {x, y}] >> >> [thousand of lines deleted] >

**References**:**the ellipse and the circle***From:*"Jack Kennedy" <jack@realmode.com>